Hi all.

NB. ----------------------------------------------------------
NB.        Vector function
NB.    vf(x,y,z) = (x^2*y^3;  2*x^2*y^3 + 4*y*z^2; y*z^2)
NB. ----------------------------------------------------------
fv=:3 : 0
 'a b c'=.y
 >((*:a)*b^3); (((2*(*:a)*b^3))+(4*b**:c)); (b**:c)
)


NB. ----------------------------------------------------------
NB.       Jacbian of vector function
NB. ----------------------------------------------------------
det=:-/ .*
Det=:det@
jac=:D.1 Det


NB. --------------------------------------------------------------------
NB.       Jacbian of vector function fv  at point (1;2;3)
NB. --------------------------------------------------------------------
fv jac 1 2 3

Answer:

_5.1159089799171479e_6   Must be   0
i.e accuracy of derivative calculations:  6 correct decimal digits (float32)

In what way to make better derivative calculation accuracy? 
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